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Superintendent Carol R. Johnson and the Boston School Committee are treading cautiously as they weigh how to overhaul the way students are assigned to schools, a hot-button issue that has polarized parents, community activists, and political leaders in the past.

“I think that for us to have a very well-designed process and thoughtful communication we need to make sure we take the time so we are prepared,’’ said Johnson. “It’s a very complex issue. . . . The last time we did this it was not well received.’’

This would be Johnson’s third attempt to change the city’s student assignment system. The two previous attempts, developed by central office administrators in fall 2008 and then again in winter 2009, fell apart amid heated public opposition.

Last April, Johnson announced that the latest effort would include a robust public engagement period. At that time, Johnson said the process would encompass 18 months and would be divided into two phases.

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The first phase, completed last summer, aims to make applying to schools more welcoming and less cumbersome. The changes included such measures as providing employees at school registration sites with more customer service training and extending registration hours.

The second phase would tackle fundamental changes that would affect which schools students could get into. To encourage community input, Johnson said, she is examining the possibility of putting together an advisory board that would represent a spectrum of viewpoints, from those who favor a system based on neighborhood schools to those who want a system that allows families to choose from a number of schools.

“It definitely needs to be a process that is driven by the community in partnership with us,’’ Johnson said in an interview.

In a series of articles this year, the Globe chronicled 13 families as they navigated the city’s student-assignment system, in which classroom seats are doled out through a computer algorithm. Many parents interviewed expressed frustration with the system, in which competition can be fierce because too many lower-tier schools are mixed in with the good ones.

Johnson began pursuing changes after Mayor Thomas M. Menino vowed in his 2008 State of the City address that the School Department would change student assignment to save millions of dollars in busing costs.

The city is currently divided into three regions, providing parents and students a choice of roughly two dozen elementary, middle, and kindergarten-through-eighth-grade schools. (High schools are open to students across the city.)

When the three zones were implemented in 1989, replacing a court-ordered forced-busing plan to desegregate the city’s schools, the creators anticipated that as schools improved academically the three zones would be replaced in a few years with nine smaller assignment areas.

But every attempt to create smaller zones over the last two decades has failed because there have not been enough high-quality schools to go around. Some neighborhoods, such as West Roxbury, have a strong selection of solid-performing schools, while Roxbury and some other areas have a concentration of the worst-performing schools in the state.

That reality will loom over the process as the School Department again assesses the feasibility of creating smaller zones.

Another potential stumbling block is that some areas of the city could lack enough school buildings to accommodate all the children who live there, while other areas of the city could wind up with too many schools, depending on how the boundaries are drawn.

Johnson’s previous attempt to redraw the zones, which would have resulted in five assignment areas, ran into problems on both fronts.

Many civil rights advocates and an analysis by the Globe found that two of the proposed zones would have a disproportionate share of low-achieving schools, while Johnson later revealed that at least two zones lacked enough seats for all the students.

“I certainly think there can be some improvements to student assignment and some [transportation] savings, but what we can’t do is adopt a plan that increases inequity,’’ said Kim Janey, senior project director for the Boston School Reform Initiative at Massachusetts Advocates for Children. “We cannot be left with a system of haves and have-nots.’’

Given the uneven distribution of good-quality schools, the city should still continue to offer some level of choice in any new student-assignment system, said Neil Sullivan, executive director of the Boston Private Industry Council, who was one of the creators of the three-zone system.

“Choice is a powerful driver of excellence,’’ said Sullivan, noting that it should compel underchosen schools to revamp programs and boost student achievement to attract students and parents.

Sullivan said he believes there are more good schools now than two decades ago and that Johnson appears to be making progress in creating more.

Two years ago, Johnson designated a few dozen low-achieving schools in a large swath of the city that includes Roxbury and a part of Dorchester for intensive intervention.

She also has expanded successful schools, shut down some failing schools, and made aggressive overhauls of 11 schools designated as underperforming by the state in March 2010, ushering in new programs and replacing teachers and principals at several of those schools.

Myriam Ortiz, executive director of the Boston Parent Organizing Network, said she believes students and parents now have a wider range of good-quality schools to choose from.

But she is concerned that many schools lack enough teachers, supplies, and materials, a plight that could prevent them from accelerating achievement.

Boston is among many large urban districts nationwide that have grappled with the thorny issue of student assignment, a mechanism once used to ensure racial diversity in schools until federal court rulings questioned the legality of the practice. (The Boston School Committee voted in 1999 to stop using race as a factor in its system.)

Two years ago, Seattle scrapped a system allowing parents to pick from a wide array of schools and replaced it with neighborhood schools, in part to reduce busing costs and to make the process of registering for schools much easier.

Now, enrollments are rising.

San Francisco changed its student-assignment system two years ago. While the new system still allows parents to choose schools, it no longer uses socioeconomic factors to fill classroom seats when demand exceeds capacity.

Instead, it looks at different “tie-breakers,’’ such as whether the student lives near the school or has a sibling there.

In Boston, Janey said, the public schools will need patience to develop a new system.

The Rev. Gregory Groover, chairman of the School Committee, said the panel is committed to reviewing student assignment.

“We need to look at the assignment system and where it needs to be enhanced,’’ Groover said. “It will be an extensive review.’’

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